Question

$v _ { e }$ and $v _ { p }$ denotes the escape velocity from the earth and another planet having twice the radius and the same mean density as the earth. Then

• A. $v _ { e } = v _ { p }$
• B. $v _ { e } = v _ { p } / 2$
• C. $v _ { e } = 2 v _ { p }$
• D. $v _ { e } = v _ { p } / 4$

Answer 1

Answer: (B)

$v _ { e } = v _ { p } / 2$

Answer 2

$v _ { e } = \sqrt { \frac { 2 G M } { R } } = R \sqrt { \frac { 8 } { 3 } \pi G \rho }$

If mean density is constant then $v _ { e } \propto R$

$\frac { v _ { e } } { v _ { p } } = \frac { R _ { e } } { R _ { p } } = \frac { 1 } { 2 }$⇒ $v _ { e } = \frac { v _ { p } } { 2 }$